Magic emission decay

Figure 7.3 Magic-angle emission decays of HAN in water and in the presence of mM of CDs. The inset shows the emission spectra of HAN in water and complexed to CDs [82-84].

Very few nuclides with Z < 60 emit a particles. All nuclei with Z > 82 are unstable and decay mainly by a-particle emission. They must discard protons to reduce their atomic number and generally need to lose neutrons, too. These nuclei decay in a step-by-step manner and give rise to a radioactive series, a characteristic sequence of nuclides (Fig. 17.16). First, one a particle is ejected, then another a particle or a (3-particle is ejected, and so on, until a stable nucleus, such as an iso tope of lead (with the magic atomic number 82) is formed. For example, the uranium-238 series ends at lead-206, the uranium-235 series ends at lead-207, and the thorium-232 series ends at lead-208. 

Fisz, J. J. (2007). Another look at magic-angle-detected fluorescence and emission anisotropy decays in fluorescence microscopy. J. Phys. Chem. A 111, 12867-70. 

Alpha (a.) decay. As we shall see later, the alpha particle, which is a helium nucleus, is a stable particle. For some unstable heavy nuclei, the emission of this particle occurs. Because the a particle contains a magic number of both protons and neutrons (2), there is a tendency for this particular combination of particles to be the one emitted rather than some other combination such as s3Li. In alpha decay, the mass number decreases by 4 units, the number of protons decreases by 2, and the number of neutrons decreases by 2. An example of alpha decay is the following ... 

The magic numbers which impart stability to a nucleus are 2, 8, 20, 28, 50, 82 or 122. The isotope, 39K, has a magic number equal to its number of neutrons, so it is probably stable. The others have a larger neutron-to-proton ratio, making them neutron-rich nuclei, so 40K and 41K might be expected to decay by beta emission. In fact, both 39K and 41K are stable, and 40K does decay by beta emission. 

Why does /3 decay occur Well, stable nuclei have stable ratios between the proton number and neutron number. These ratios are nontrivial to predict, and are arcane to the extent that they include the concept of magic numbers. 1 Beta-minus emission occurs because some nuclei have too many neutrons therefore /3 decay is energetically favorable, resulting in a reduction in the neutron-to-proton ratio. 

Due to the topology of the island, superheavy nuclei should decay by spontaneous fission, either immediately or after a sequence of other decay steps. In a detailed theoretical exploration [12] of the Z-N plane around the island, the longest-lived nuclide again turned out to be Z=110, A=184, decaying with 3xl09 y half-life by a-particle emission to 290108. From there, two subsequent (T-transitions should lead via 290109 to 290110, where the chain should terminate by spontaneous fission with 140 d half-life. The doubly magic 298114, half-life 790 y, should also decay into 290110 by two a-particle emissions via 294l 12 as the intermediate. 

The plane-polarized light pulses characteristic of mode-locked lasers also provide an ideal excitation source for time-dependent fluorescence depolarization studies although conventional excitation sources can be used. If the rotational relaxation time of the excited molecule is comparable to its fluorescence decay time, then the vertical (I ) and horizontal (Ix) components of the fluorescence decay observed through suitable polarizers following excitation by polarized li t pulses, may be analysed to provide information concerning the size and motion of die molecule and Sect. 5. However, if only the true fluorescence decay characteristics are of interest it is necessary to compensate for these emission anisotropy effects Perhaps the simplest technique is to analyse only that component of fluorescence emitted at 54.7° to the direction of pdarization of the excitation source, the so-called magic-angle ... 

In order to examine the properties of the fluorescent states for the dendrimers more closely, fluorescence decay times for all first generation dendrimers were determined in toluene by single-photon timing detecting the emission under magic angle condition. 

The nucleus would thus seem to consist of independrat substructures of neutrons and protons, with each type of nucleon paired off as far as possible. Further, the nucleons obviously grouped together in the magic numbers. From the decay of radioactive nuclei we know that the total decay energy (Q-value) of any particular nuclide has a definite value. Moreover, y-emission from any particular nucleus involves discrete, definite values. These facts resemble the quantized emission of electromagnetic radiation (X-ray, UV, visible light. 

Excited bound states of atoms are one of the simplest examples of unstable quantum states which decay radiatively into the continuum of possible one-photon states of the electromagnetic field in free space. The search for a satisfactory theoretical explanation of the line frequencies and intensities of photon emission spectra at the beginning of the last century eventually culminated in Heisenberg s "magical paper" from July 1925 [1, 2] and in the development of modern quantum mechanics [3-6]. Although basic aspects of this spontaneous decay process have already been described theoretically in an adequate way in the early days of modem quantum mechanics [7,8], interestingly, some of its time-dependent dynamical aspects are still of topical current interest. 

Seeking stability, proton-rich nuclei decay by emission and/or electron capture, and the neutron-rich nuclei by p emission into their isobars. Near magic numbers, the nuclei are more or less spherical far from them, they are usually deformed. 

In the event that one wishes to measure only the fluorescence decay times of a sample, but is forced to make the measurement with polarizers present, it is imperative that the emission polarizer be oriented at an an e of 54.7° 55° with respect to the vertical excitation orientation (the so-called magic angle ) in order to correct for the presence of the polarizers. Otherwise, as the apparent decay rates of the horizontal and vertical fluorescence components are due to both the depletion of the excited state population and to fluorophore motion (as we mentioned in Section 2.5.1), the measured lifetimes will be incorrect... 

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